Radio frequency (RF) power amplifier (PA) design using Gallium Nitride (GaN) transistor technology requires accurate device models in order to maximise performance and reduce development time. The current state-of-the-art frequency-domain behavioural focus on linear quadratic approximations the polyharmonic distortion (PHD) formalism. However, approximation suffers from poor accuracy under load...

We recall four open problems concerning constructing high-order matrixexponential approximations for the infimum of a spectrally negative Levy process (with applications to first-passage/ruin probabilities, the waiting time distribution in the M/G/1 queue, pricing of barrier options, etc). On the way, we provide a new approximation, for the perturbed CramérLundberg model, and recall a remarkabl...

A novel application of the Padé approximation is proposed in which the Padé approximant is used as an interpolation for the small and large coupling behaviors of a physical system, resulting in a prediction of the behavior of the system at intermediate couplings. This method is applied to quarkonium systems and reasonable values for the c and b quark masses are obtained. PACS: 11.15.Me, 11.15.T...

It is well known that the bilinear transform, or first order diagonal Padé approximation to the matrix exponential, preserves quadratic Lyapunov functions between continuous-time and corresponding discrete-time linear time invariant (LTI) systems, regardless of the sampling time. It is also well known that this mapping preserves common quadratic Lyapunov functions between continuous-time and di...

We consider multipoint Padé approximation to Cauchy transforms of complex measures. We show that if the support of a measure is an analytic Jordan arc and if the measure itself is absolutely continuous with respect to the equilibrium distribution of that arc with Dini-smooth non-vanishing density, then the diagonal multipoint Padé approximants associated with appropriate interpolation schemes c...

The standard inverse scaling and squaring algorithm for computing the matrix logarithm begins by transforming the matrix to Schur triangular form in order to facilitate subsequent matrix square root and Padé approximation computations. A transformation-free form of this method that exploits incomplete Denman–Beavers square root iterations and aims for a specified accuracy (ignoring roundoff) is...

Coverage probability is one of the most important metrics for evaluating the performance of wireless networks. However, the spatial stochastic models for which a computable expression of the coverage probability is available are restricted (such as the Poisson based or α-Ginibre based models). Furthermore, even if it is available, the practical numerical computation may be time-consuming (in th...

Sorokin gave in 1996 a new proof that π is transcendental. It is based on a simultaneous Padé approximation problem involving certain multiple polylogarithms, which evaluated at the point 1 are multiple zeta values equal to powers of π. In this paper we construct a Padé approximation problem of the same flavour, and prove that it has a unique solution up to proportionality. At the point 1, this...